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Errors of stress numerical integration for cross-sections with straight and curved boundaries

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Wybrane pełne teksty z tego czasopisma
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Języki publikacji
EN
Abstrakty
EN
Internal forces are integrals of stress in a section area. Integrating the stress for an arbitrary cross-section shape and for the nonlinear stress-strain law σ(ε) is tedious and the use of the boundary integral approach can simplify computations. Numerical integration when applied to the computations of such integrals introduces errors in many cases. Errors of numerical integration depend on the adopted integration scheme, the type of σ(ε) and the shape of the cross-section boundary. In the case of adaptive numerical integration what is very important are the properties of the sequence of errors produced by a given integration scheme in the increasing order of the numerical quadrature or the increasing number of subdivisions. This paper analyses errors caused by different integration schemes for the typical σ(ε) either for a straight or curved boundary. Special attention is paid to the properties of the error sequence in each case. The outcome of this paper is important from the viewpoint of the reliability and robustness of the software developed for nonlinear simulations of bar structures.
Rocznik
Strony
153--176
Opis fizyczny
Bibliogr. 19 poz., rys., tab., wykr.
Twórcy
autor
  • Cracow University of Technology Institute for Computational Civil Engineering Warszawska 24, 31-155 Cracow, Poland
Bibliografia
  • [1] G. Alfano, F. Marmo, L. Rosati. An unconditionally convergent algorithm for the evaluation of the ultimate limit state of RC sections subject to axial force and biaxial bending. Int. J. Numer. Meth. Eng., 72(8): 924–963, 2007.
  • [2] J.L. Bonet, M.H.F.M. Barros, M.L. Romero. Comparative study of analytical and numerical algorithms for designing reinforced concrete sections under biaxial bending. Comp. Struct., 84(31–32): 2184–2193, 2006.
  • [3] J.L. Bonet, M.L. Romero, P.F. Miguel, M.A. Fernandez. A fast stress integration algorithm for reinforced concrete sections with axial loads and biaxial bending. Comp. Struct., 82(2–3): 213–225, 2004.
  • [4] L. Cedolin, G. Cusatis, S. Eccheli, M. Roveda. Capacity of rectangular cross sections under biaxially eccentric loads. ACI Struct. J., 105(2): 3–4, 2008.
  • [5] A.E. Charalampakis, V.K. Koumousis. Ultimate strength analysis of composite sections under biaxial bending and axial load. Adv. Eng. Softw., 39(11): 923–936, 2008.
  • [6] C.G. Chiorean. Computerised interaction diagrams and moment capacity contours for composite steel-concrete cross-sections. Eng. Struct., 32(11): 3734–3757, 2010.
  • [7] V. Dias da Silva, M.H.F.M. Barros, E.N.B.S. Júlio, C.C. Ferreira. Closed form ultimate strength of multirectangle reinforced concrete sections under axial load and biaxial bending. Computers and Concrete, 6(6): 505–521, 2009.
  • [8] L. De Vivo, L. Rosati. Ultimate strength analysis of reinforced concrete sections subject to axial force and biaxial bending. Comput. Method Appl. M., 166(3–4): 261–287, 1998.
  • [9] M. Di Ludovico, G.P. Lignola, A. Prota, E. Cosenza. Nonlinear analysis of cross sections under axial load and biaxial bending. ACI Struct. J., 107(4): 390–399, July – August 2010.
  • [10] A. Fafitis. Interaction surfaces of reinforced-concrete sections in biaxial bending. J. Struct. Eng. ASCE, 127(7): 840–846, 2001.
  • [11] B.A. Izzuddin, A.A.F.M. Siyam, D. Lloyd-Smith. An efficient beam-column formulation for 3D reinforced concrete frames. Comp. Struct., 80(7–8): 659–676, 2002.
  • [12] A. Matuszak. Algorithm for determining compressed region of cross-section and computing its moments of area. Tech. Transact., (3-B): 89–111, 2012.
  • [13] A. Matuszak, P. Pluciński. Accuracy of cross-section stress numerical integration by boundary integration formulae. In: T. Łodygowski, J. Rakowski, P. Litewka [Eds.], Recent Advances in Computational Mechanics, pp. 111–120. CRC Press, 2014.
  • [14] L. Pallar´es, P.F. Miguel, M.A. Fernández-Prada. A numerical method to design reinforced concrete sections subjected to axial forces and biaxial bending based on ultimate strain limits. Eng. Struct., 31(12): 3065–3071, 2009.
  • [15] V.K. Papanikolaou. Analysis of arbitrary composite sections in biaxial bending and axial load. Comp. Struct., 98–99: 33–54, 2012.
  • [16] L. Rosati, F. Marmo, R. Serpieri. Enhanced solution strategies for the ultimate strength analysis of composite steel-concrete sections subject to axial force and biaxial bending. Comput. Method Appl. M., 197(9–12): 1033– 1055, 2008.
  • [17] M.G. Sfakianakis. Biaxial bending with axial force of reinforced, composite and repaired concrete sections of arbitrary shape by fiber model and computer graphics. Adv. Eng. Softw., 33(4): 227–242, 2002.
  • [18] J.B.M. Sousa, C.F.D.G. Muniz. Analytical integration of cross-section properties for numerical analysis of reinforced concrete, steel and composite frames. Eng. Struct., 29(4): 618–625, 2007.
  • [19] D. Zupan, M. Saje. Analytical integration of stress field and tangent material moduli over concrete cross-sections. Comp. Struct., 83(28–30): 2368–2380, 2005.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-5f6d2f97-67c2-470e-a288-6ed5322e8231
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